Temporal Knowledge Graphs (TKG) store events that evolve dynamically over time. Due to the inherent incompleteness of TKGs, Temporal Knowledge Graph Completion (TKGC) is required to predict missing facts and complete the knowledge graph. Existing TKGC methods overlook the structural similarities between different entities and fail to fully exploit the structural dependencies of relations. Therefore, this paper proposes a relation-symmetric structure contrastive learning with relation-aware masking for temporal knowledge graph completion (SyM-TKGC). The method identifies semantically similar entities through relation-symmetry patterns and enhances their representations via contrastive learning. Additionally, we employ relation co-occurrence graphs to capture structural dependencies while applying stochastic edge masking to suppress irrelevant connections, thereby preventing over-reliance on non-causal relation patterns. Experimental results demonstrate that the SyM-TGKC model achieves superior MRR performance on three benchmark datasets, with improvements of 1.84%, 1.47%, and 23.7% over existing methods, thereby achieving state-of-the-art performance.